ΔE 15.6, loose: different enough that you should pick on purpose. Willow Bark is a little darker, more muted than Tyrian Navy.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Willow Bark is a little darker, more muted than Tyrian Navy.
The same difference applies the other way round: Tyrian Navy is a little lighter, more saturated.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Tyrian Navy on the colour wheel See Willow Bark on the colour wheel
All matches: Tyrian Navy equivalents · Willow Bark equivalents